Simulating Competition and Logistic Growth
Resource limits bend exponential curves into S-shaped logistic curves. The fourth in a series on evolution.
Made with Blender and python.
Github: github.com/Helpsypoo/primer
Special thanks to supporters on Patreon, especially:
Jordan Scales
世珉 匡
Eric Helps
Ben Kamens
Christy Serbus
Sean Barker
Support Primer on Patreon:
/ primerlearning
For discussion and updates
- Discord: / discord
- Reddit: r/primerlearning
- Twitter: @primerlearning
- Facebook: primerlearning
Streaming myself working on these monstrosities:
- Twitch: / primerjustin
More on logistic growth on Khan Academy:
www.khanacademy.org/math/ap-c...
www.khanacademy.org/science/h...
License information:
Creative Commons 4.0 (CC-BY-NC). More info at creativecommons.org/licenses/...
Speaking of attribution:
The 3D bunny model comes from the Stanford Computer Graphics Laboratory: graphics.stanford.edu/data/3Ds...
The music is "Summer Days" by Kai Engel, distributed under a CC-BY-NC license via the Free Music Archive. freemusicarchive.org/music/Kai...
Several other inputs into the graphics are from public domain contributions to www.blendswap.com.
Пікірлер: 830
sometimes youtube algorithm really gives you the good stuff like this
@Blobbyboi986
5 жыл бұрын
You are correct
@timbo3406
4 жыл бұрын
Yeah!
@thinboxdictator6720
4 жыл бұрын
if it is sometimes,then it is more likely a mistake
@nicosalsa21
4 жыл бұрын
Then we get actually happened videos only
@dsi-films1264
4 жыл бұрын
Yeah your right
A number of people have commented that at 5:22, the green population should be expected to beat out the blue population because the blue population suffers from mutations while the green population benefits from them. That effect is real, but it's too small to tip the scales, and I determined it was too complex for the main message of the video. But because some people are interested, I thought I'd lay it out in more detail here. Only 1% of replications by blue creatures produce a green creature (4:52), and another 1% produce orange creatures. This means blue's replication rate is effectively only 98% of the stated value. 9.8% instead of 10%. The green population gets an expected influx of creatures each time step equal to 0.001 (a tenth of a percent) times the number of blue creatures. Here's a desmos graph of the expected changes per time step for blue and green, from the equation in the video. (The green equation has an added term for bonus creatures from blue's mutations.) www.desmos.com/calculator/zhig0dcftg x is the number of blue creatures, and there are sliders for the other parameters if you want to play with them. N is the total, and N-x is the number of green creatures. We can see that when there are 49 or more blue creatures we expect to gain green creatures and lose blue creatures. And if there are 44 or more blues, we expect to lose more blues than greens. But for any number of blues less than this, we expect green to do worse. Green is never expected to outnumber blue. This all assumes no oranges. The fact that the functions add to less than zero for any value reflects the fact that orange is gaining in any of these scenarios. So it's true that in this setup blue suffers losses from mutations to different colors while green benefits, but the magnitude of this effect with the given parameters is too small to make up the difference in base replication chance between green and blue. Additional sims I ran reflect this fact, with green regularly losing, but I chose to animate the first sim I ran because it was a good reminder of how chaotic this system is. I appreciate folks commenting with a critical eye, and this will help me know what to explain more clearly vs what to gloss over in future videos. It was also kind of fun to make the desmos graph. If you like it and want to see more desmos graphs when relevant to other videos, please reply to this comment and tell me so!
@mehdibouchaffra868
5 жыл бұрын
Thanks!
@homeyworkey
5 жыл бұрын
new subscriber here, whatever u put out i think im going to watch either way :)
@SaganIII
5 жыл бұрын
More of this ! 🤤
@2haha447
5 жыл бұрын
But dosn't this also influence the "death rate" because blue lose every mutation one who can not replicate you could maybe give both yellow and green a 1% mutation rate to get blue idk it is just an idea
@Kamushy
5 жыл бұрын
Primer wow
The way the blobs wiggle their hands.
@Isvoor
5 жыл бұрын
The way the blobs win our hearts.
@henryg.8762
4 жыл бұрын
'hands'
@williamhuynh869
4 жыл бұрын
The derp.... I love derpy stuff, like Quagsire and these blobs
@awhahoo
3 жыл бұрын
They vibin
@bigmoniesponge
3 жыл бұрын
@@henryg.8762 I need to watch his video now “5 ways NOT to think.”
My God, In collage I was unable to figure out from where numbers comes out and memorize all stuff related to logistic growth without understanding it at all just to pass my matlab laboratories. It's so hard to explain this so simple. Thank you, channels like this deserve gold medal and monetization factor of x100
@erwinmoreno23
5 жыл бұрын
Hahah your last sentence is what all of us think but couldnt quite express
@rogeronslow1498
5 жыл бұрын
That's the problem with most universities. They produce graduates that are good at remembering stuff, not necessarily understanding stuff.
@poofy6959
4 жыл бұрын
Collage btw
@cqrcin0
4 жыл бұрын
*College :\
@umbuchscui
4 жыл бұрын
College* And I’m 10
This is one of the only channels that I will drop everything to watch when a new video comes out. Love it!
@MystGames
5 жыл бұрын
nigga
@bestbread3446
5 жыл бұрын
rude
@MystGames
5 жыл бұрын
@@bestbread3446 not really, since it's not directed at anyone or anything. CHECK YO' PRIVILEGE, SON
@vanthonvenus
5 жыл бұрын
would you drop your child?
@MystGames
5 жыл бұрын
LillyCookies DDAENG no, but im sure you were dropped as a child.
If it's too crowded, you could also just snap your fingers
@eclipserepeater2466
5 жыл бұрын
At which point that whole "logistics curve" thing would quickly bring the population back up to carrying capacity. No matter how powerful the snap, its effects are ultimately temporary. :P
@BoneAppleTea
5 жыл бұрын
@@eclipserepeater2466 I know, Thanos was not a mathematician haha
@Wm7forthewin
5 жыл бұрын
+DEMON XD sorry boys we took over the planet and have gone to the moon and invented the internet
@brendaajamu7152
5 жыл бұрын
Love that sub
@rage_2000
5 жыл бұрын
*Orange blobs appear* Blue blobs: _I don’t feel so good_
I'm a fan for the excited orange blob
@cgmelody6422
5 жыл бұрын
Nick Louie bandwagon fan
@Ziess
4 жыл бұрын
I'd like this but it's at orange blob's favourite number, 69.
@Poffean
4 жыл бұрын
@@Ziess 87, let's get it to 420
@extaponts2402
4 жыл бұрын
Me too
@outofcontext728
4 жыл бұрын
You mean scp 999
You should simulate the predator-prey model I think it would be really fun
@bodbn
5 жыл бұрын
Blue blobs being sore losers
@AltAccount-ko3pp
4 жыл бұрын
I'm pretty sure he has done this in a later video now
@biglefteye5017
4 жыл бұрын
Kiritsu yes
@ChaosAbandon
4 жыл бұрын
He did
@miniaturejayhawk8702
4 жыл бұрын
@MsBizzyGurl na its more like gis first natural selection simulation. There he made it that when a blob was 20% bigger than the others it could simply eat them.
I love how when you run the simulations it's 3d models just sliding along a wall
@purple_sky
4 жыл бұрын
I believe it's a flat plane viewed from above, and they are just looking up because they know how to smile at the camera
Can't believe I've missed out on this superb content until now ! Keep up the good work man !
@colleen9493
5 жыл бұрын
Yeah same. Simulating natural selection just showed up in my recommended.
@cartor7892
5 жыл бұрын
Same just found this channel yesterday
so thanos should've just modified creature's stats to reach the ideal equilibrium at some point in time instead of killing the half of everything which is only a temporary solution. not so smart huh
@MarkAlcarezBoston
4 жыл бұрын
Yes
@aquaphoenix-mt2iv
4 жыл бұрын
He'd have to increase birth rates for almost all creatures (except humans, since they're the problem-) And increase how quickly plants grow (to sustain current human populations, and the soon to be increased animal populations from increasing their birthrates) And since he can't do both of those in one snap (those are seperate actions after all), he'd have to snap twice. Which would kill him more than likely. Also those variables would have to be very precisely changed So.. no, he really couldn't fix it that way. I do agree that decreasing population size was the dumbest possible solution though
@TooHarshForYou
3 жыл бұрын
Even if he didnt add , there was still a n equilibrium point , the thing is humans modified earth to increase ita carrying capacity to their own good and thus they influenced their own stats and caps
@matyaskassay4346
3 жыл бұрын
but don't forget that in real life the "stats" are determined by the environment of the creatures, and aren't fixed unconditionally.
@user72974
3 жыл бұрын
This guy literally just debunked Thanos.
"Sorry, buddy." Orange blob: *blank face*
Clear and very well animated! For the mathematically inclined, you can read delta as the derivative of N with respect to time, since it is the variation of N. Thus, before adding the crowding term, you get dN/dt = aN, a differential equation whose solution is indeed exponential, N = exp(at) + c. By adding the crowding term, you get dN/dt = aN^2 + bN, and the solution to that differential equation is the logistic function, as stated.
@PrimerBlobs
5 жыл бұрын
++ Thanks for spelling it out. :)
@hubierti
5 жыл бұрын
Help me out here, if dN/dt = aN, then the integral of dN/dt with respect to t is N. Thus, integral of aNdt = aNt = N, right? What am I missing?
@XenophonSoulis
5 жыл бұрын
Thank you!
@kvackkvackfrisk
5 жыл бұрын
@@hubierti No, since N actually is a function of t itself (you could write our differential equation as N'(t) = aN(t)) you can't just leave it be when you integrate with respect to t - what we're looking for is a function whose derivative has the original function as a factor. And in fact, the only function f(t) whose derivative f'(t) = some constant * f(t) is the exponential function, and the derivative of e^ax = a*e^ax so the solution must be, like Vincent stated, N(t) = e^at + C since this gives N'(t) = a*e^at = a*N(t).
@Kryo_Ghost
4 жыл бұрын
I am smol brain and i have no ide wat haf of dis is
This reminds me of some of my favorite teachers over the years. You take the time to explain a concept in detail, and show every step of your work, while explaining WHY it's changing and how it's affecting everything else. You also recap things we've gone over before, and recap when you finish a concept. It's wonderful, and honestly, has pushed me to add physics classes to the bio classes i was planning on when I return to school. You've rekindled my love of math, and I applaud you for it. Thank you.
"We've seen that creatures can grow exponentially-" (flip flop) "But in the real world-" (stop) "A realistic growth curve would look something like this." (HOW CAN YOU DO THIS TO ME)
Thanos’ plan layout when trying to *save the universe* .
@yzraeloa3787
4 жыл бұрын
ellathon22 this actually shows how futile Thanos strat is. Population would grow back in no time and even promote a higher replication ratio
@TheRedMooncorp
4 жыл бұрын
@@yzraeloa3787 Plus you have an initial universal famine, since most logistics will be severly damaged due to the loss of half the officials, half the technicians, half the farmers etc. Thanos never really thought this through at all^^
@IamCoalfoot
4 жыл бұрын
@@TheRedMooncorp It took me about five seconds of thought when I heard his plan to realize he'd spent about zero seconds on it.
@TheRedMooncorp
4 жыл бұрын
@@IamCoalfoot I feel you. I mean even choosing specifically half is so stupid. Even if Thanos would be right, the optimal number of deaths would differ from world to world, but sure let's treat a well organized society with population controlls, a new colony with 500 people and a sprawling over populated world of slums the same 😂😅
@cooperwright9515
4 жыл бұрын
TheRedMooncorp population controls are a meme
Thanks - I've been looking forward to this video for a while - you have a style that makes it very easy to listen to and understand. I'm looking forward to what comes next.
@PrimerBlobs
5 жыл бұрын
Thanks, I really appreciate the kind words.
Sooo... you spent the first 3/4 of this video explaining the very basics of calculus? I'm not complaining. In fact I'm very glad you are doing this because it is very useful in explaining these kinds of situations where the rate changes over time. So good job, plus you made it more interesting than any lecture could be.
Thanos should watch your videos.
It's been 50 days! We miss your videos!
@PrimerBlobs
5 жыл бұрын
Haha, thanks for the enthusiasm. Rest assured that more are coming. I'm getting impatient too. :P
@munzeralseed
5 жыл бұрын
:D
@theprofessor1554
4 жыл бұрын
@@PrimerBlobs :D
@Hansgilhaus
4 жыл бұрын
Plz do a video on simulation of life and why these ameobas are pear shaped
@Hansgilhaus
4 жыл бұрын
They ameobas cuz they look squidgy and there hands stretch from their bodies so there pseudopods
Wowwww I wished my calc teacher taught it like this when we learnt logistical functions. Never realized why dN/dt=N is exponential and dN/dt=-N^2 logistical.
@b1rd1e81
5 жыл бұрын
I knew that it was exponential only from integration, cool to see the visuals though
@h_3795
5 жыл бұрын
B1rd1e yeah I know how to integrate it but it didn’t make sense conceptually.
@dvirkomlosh4152
5 жыл бұрын
@@h_3795 can you maybe explain? I really wanna know how to get the function of N from the Delta function
@h_3795
5 жыл бұрын
dvir komlosh shoot idk man. I can give you the proof with integration but idk conceptually. But here’s what I think. The reason why tho that dN/dt=N is exponential is that it doesn’t have to move to the right in order to increase faster. Simply increasing makes it increase faster. With dN/dt=t, which results in a quadratic, much slower, you have to increase t in order to increase faster, which lowers the slope.
@h_3795
5 жыл бұрын
dvir komlosh oh I’ve just figured it out. You know that the derivative of y=e^x is e^x, so dy/dx e^x=e^x. Since y=e^x, dy/dx=y
Ooh differential equations in disguise
@PrimerBlobs
5 жыл бұрын
Shh
@buygeorgeivegotit7203
3 жыл бұрын
I will reply to not shh
@buygeorgeivegotit7203
3 жыл бұрын
And use my home account tomorrow
@awhahoo
3 жыл бұрын
@@buygeorgeivegotit7203 F
I'm horrible at maths and science so I don't always understand all the numbers in these videos but all the concepts are really well explained and easy to grasp with a second watch and well-worded google searches. The simulations are also really interesting, easy to follow, and incredibly entertaining, and all of this combines to make your videos some of the best I've seen on KZread- thank you so much!
Oh how my AP Calculus teacher ruined variable specification for me, I know that if I didn't specify N' = Delta when doing a project like this I'd have gotten tossed out a window or something for not defining my variables sufficiently. Other than that petty observation which most people would just be able to figure out if they're not baboon-tier, this video is genuinely an excellently animated, excellently voiced, and phenomenally descriptive example of the fact that there truly are still amazing content creators on this platform. This will be the first patreon that I support, and I wholeheartedly look forward to your next videos in the future!
@peterlewis2178
2 жыл бұрын
I love how you condescendingly call people who are less mathematically gifted or educated "baboon-tier". It says a lot about you that you consider people to be tiered in that way, and consider yourself in a superior "tier".
I absolutely adore this series of videos, I can't watch enough of them! please keep making them
I should be studying... but as a former biology student, and as I'm fascinated by genetics, I just can't stop watching this series
Never forget that he retconned where the orange blobs came from. Personally, I prefer the original lore, and I'm not calling it 'Legends' or some dumb name like that.
@alkali5841
3 жыл бұрын
TELL US
Thanks for giving me a solid base to my next simulation game.
*Edit* : read response by channel before liking my comment ;) I doubt that green won because of luck in the simulation at 5:19. Blue loses offsprings to mutation (both orange and green) which makes blue worse than the stats suggest. Additionally green has a higher birthrate as blue mutates into green. Although I have to admit that you didn't show the mutation rates, so they could be small enough to be negligible. I think for a better comparison both orange and green could mutate back to blue with the same likelyhood.
@vantutri9571
5 жыл бұрын
This white haired guy is right
@PrimerBlobs
5 жыл бұрын
I didn't add a label for the mutation rate, but I did say that orange and green each come out of 1% of blue's mutations. So blue is still 98% as good as the written stats suggest.
@vantutri9571
5 жыл бұрын
@@PrimerBlobs yeah 98% is only for one generation though. Blue is destined to extinction
@vantutri9571
5 жыл бұрын
@@PrimerBlobs oh your videos are lovely and almost unique btw. Can you make a video about yourself, how do you make these videos and how long does it take? Thanks a lot
@georgplaz
5 жыл бұрын
@@PrimerBlobs You are right. I missed that! And yes, 1% is pretty negligible. The mutation rate does really "feel" a lot higher though. But I'll take your word!
0:12 *_"Sorry buddy."_*
I have my BA in biology I wish a few of my professors would have used something like this, a lot of people have a hard time understanding population growth. Very informative
I just stumbled upon these videos and I really /really/ enjoy how simplified they are. I enjoy watching these kind of things. Keep up the good work
0:28 could of been a really nice city landscape ya know
I never understood graphs and stuff, like parabels (i don't know if that's the right word, i'm german, so i don't know the special terms for that) in school, but you are really outstanding when it comes to explaining something. Great job man!
Please don't stop making videos, your videos are the beauty of KZread and are really satisfying, enjoyable and interesting.
Those videos are amazing, very high quality. Thank you and great work!
Man your videos are fantastic, I'm sure many people would kill for more frequently released episodes
I wish there were more of these videos! They’re very interesting and informative.
This is an awesome way to grasp derivatives too wow this is an insanely clear explanation too thank you 🙏🏽❤️
I like how you explain these differential equations in such an intuitive way.
I love how this KZreadr just sprouted up with confidence and good quality. Most people start nervous and slow with no audio or something like that. I'm not saying that's a bad thing, I'm just saying that this is way better. It's awesome.
0:06 even though we have limits in the real world it’s still nice to see that the human population looks similar to that graph over the past 150-200 years
This is one of the best channels on KZread. Huge fan.
I would like to say that I absolutely LOVE this. I also love the fact that so many people are on board with this series, this topic, and this channel! It actually surprises me how many people like this stuff besides me. Thanks Primer!!! Also since you're going this high so fast you might want to put that face reveal at a higher sub level. Just saying.
I love your videos! This is going to be useful in for future for sure :) It's nothing to complicated, but you always go over things that are easy to overlook.
These videos are so simple, yet SO entertaining
Excellent quality for the visuals and commentary - great stuff!
This is so entertaining, calming and educating. Great job!
These videos are so chill and fun to watch. I'm glad I clicked on one when it was randomly recommended. I love watching the adventures of these little blobs!
Just found this channel, fantastic videos! I’ve been looking for a good educational economics channel for a while
The video, the music and the presentation of the information are excellent
I can say that this is helping me with my trapping course because you talk about the carrying capacity. Keep it up, your vids are epic.
I am so glad I found this channel It’s funny and I’m learning about something that is extremely complex easily
So calming and easy to enjoy. This is so satisfying
Really enjoying this series. Great work
I love this stuff, please keep doing it, I think your style is awesome
I always love coming and watching your videos because I always learn something from it :3
Excellent material. Very clear and informative. Great work!
So far I am loving this series.
This is like 3Blue1Brown standard quality! Good stuff man!
This guy could write codes for old school RuneScape. Lots of equations like this. Really helped me get good at math as a kid. Great vids
Finally KZread recommended something stimulating... Keep up the great content
I’m in a calc 2 class rn and just had a test on differential equations (of which logistic growth is one) and it just occurred to me that logistic growth is just the next polynomial step up from direct growth (adding one term)
Wow! I just love watching the blobs. Great animation by the way!
shoutout to my guy for putting so much work for 7 minutes of goodness
This quality videos are the reason why KZread is an amazing place
Would love to see your take on something like the rabbit and fox problem, or some other version of populations that have growth rates variant of eachother. Love the videos!
I have multiple questions: Which programming language do you use ? How do you visualize all these stats ? Where can I learn/read more about genetic algorithms, which is related to this topic? Thank you so much for the videos I like each and every one of them
KZread recommended me your videos, and I've been binging since. I've been reading a lot about world leaders, especially the suffering going on in North Korea. I've always wondered how one person can end up on top like that, and it would be really interesting to see a simulation based on these structures. I'm still getting through these videos, so I might come across it, but I've just been so fascinated in the way that the world works, which has taken me 25 years to get to this level of curiosity. I saw the doves and hawks video, and I am wondering if it's a derivative of that, but at a way larger scale. Thank you for these videos, so much food for thought. I look forward to any videos you might make in the future :~)
Nice too see all the math about probability etc. in action^^
these are really interesting videos, little tibits like this can make a morning so much better :D
Ur channel is awesome. Keep up the interesting lovely stuff!
5 seconds and I subscribed. God bless youtube recommendations for this good stuff!
You are the only KZreadr of quality
Why are these videos so fun to watch
this is the best channel to procrastinate to.
Fantastic series!
I'm binge watching all primers videos
I love your channel! awesome content. Thank you!
Very well presented. Thank you
Love your videos!
OMG these animations are soo neat
I came back to watch it again since now I understand this math!
Your content is great! Please keep on doing videos❤❤❤
All I've picked up from these vids so far is that orange is the superior race
@EugeneAyindolmah
5 жыл бұрын
G E K O L O N I S E E R D
@mememachine3029
5 жыл бұрын
Trump is Orange
@dezynjikReal
3 жыл бұрын
@@mememachine3029 you are an orange
i'm really mad you didn't simplify the bell curve into a quadratic equation. im so invested in how beautiful functions look
Fantastic channel. This will grow, a lot.
i love this channel so much
These videos make math exciting for me
This channel is amazing
Please more videos like these, from Uruguay
I learned about this channel from 3blue1brown's website, in his FAQ, the first question he answers is what does he use to animate his videos? He mentions you as an example of not only someone who took inspiration from him, but did the best in coming up with your own unique style, so I thought you were worth checking out based on that. I'm glad I did, and what's more, I liked this video so much that I've just subscribed :)
A good lesson about logistic growth without a single mention of calculus.... Impressive. Clearly calculus is still evident, but the idea was presented flawlessly without it. Good job!
I love your videos! They are pretty lovely!
Man, your content is addictive.
It's better to watch the videos in this playlist in their intended sequence. 🤜💥🤛
i love this channel bc it sceince/maths but i understand it and its fun bc its about things i will click on XD keep it up!!!!
I really hope you're a teacher somewhere. I learn more in these short videos than I did sitting in a high school class lol. The simulations and animations are top notch
Amazing videos. Question. What did you program these simulation models with? What program/coding. Thanks.
I couldn't tell at first but yes the Crowd does include the mutations. Could change based on type of eating/digestive systems.